Advertisements
Advertisements
Question
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
Advertisements
Solution
It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(–2x + 5y – 3z)2 = (–2x)2 + (5y)2 + (–3z)2 + 2(–2x)(5y) + 2(5y)(–3z) + 2(–3z)(–2x)
= 4x2 + 25y2 + 9z2 – 20xy – 30yz + 12xz
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
103 × 107
Expand the following, using suitable identity:
(x + 2y + 4z)2
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
Evaluate the following using identities:
(399)2
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
Write in the expanded form:
`(2 + x - 2y)^2`
Write in the expanded form: `(x + 2y + 4z)^2`
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Evaluate: (2 − z) (15 − z)
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
(x + y - z)2 + (x - y + z)2
Expand the following:
(3a – 5b – c)2
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
